Question

If the area (in square units) of the region under the curve of the function f(x) = 4 on the interval [1, a] is 20 square units, and a > 1, then what is the value of a?

Answers to choose from is: a) 5, b) 6, c) 8, d) 9.

Answer 1

b) 6

Explanation:

The function f(x) = 4 is simply the horizontal line y = 4. Therefore, the region bounded by the curve of the function f(x) = 4 on the interval [1, a] with a > 1 is simply a rectangle whose length is (a-1) units and width 4 units. We have been informed that the area is 20 square units, therefore we can formulate the following equation using the formula for the area of a rectangle;

Area = length * width

20 = 4(a-1)

5 = a-1

a = 6

Therefore, the value of a should be 6.